In this project, our goal is to write a software pipeline to identify the lane boundaries in a video. The steps of this project are the following:
- Compute the camera calibration matrix and distortion coefficients given a set of chessboard images.
- Apply a distortion correction to raw images.
- Use color transforms, gradients, etc., to create a thresholded binary image.
- Apply a perspective transform to rectify binary image ("birds-eye view").
- Detect lane pixels and fit to find the lane boundary.
- Determine the curvature of the lane and vehicle position with respect to center.
- Warp the detected lane boundaries back onto the original image.
- Output visual display of the lane boundaries and numerical estimation of lane curvature and vehicle position.
In [4]:
import pickle
import cv2
import numpy as np
import glob
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
%matplotlib inline
Camera Calibration¶
I started by preparing "object points", which will be the (x, y, z) coordinates of the chessboard corners in the world. Here I am assuming the chessboard is fixed on the (x, y) plane at z=0, such that the object points are the same for each calibration image. Thus, object points objp is just a replicated array of coordinates, and list of object points objpoints will be appended with a copy of it every time I successfully detect all chessboard corners in a test image. List of image points imgpoints will be appended with the (x, y) pixel position of each of the corners in the image plane with each successful chessboard detection.
In [5]:
images = glob.glob('./camera_cal/*.jpg')
print("Number of images: ", len(images))
In [3]:
# find corners
identified_img = []
objpoints = []
imgpoints = []
fig, axs = plt.subplots(5,4, figsize=(16, 10))
axs = axs.ravel()
for idx, path in enumerate(images):
img = cv2.imread(path)
# prepare object points
objp = np.zeros((9*6,3), np.float32)
objp[:, :2] = np.mgrid[0:9, 0:6].T.reshape(-1, 2)
nx = 9
ny = 6
# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
# Find the chessboard corners
ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)
# If found, draw corners
if ret == True:
identified_img.append(img)
objpoints.append(objp)
imgpoints.append(corners)
# Draw and display the corners
cv2.drawChessboardCorners(img, (nx, ny), corners, ret)
axs[idx].imshow(img)
Some images' corners can not be found due to that they have different number of corners, i.e.9x5 (see above image) rather than 9x6. I then used the output objpoints and imgpoints to compute the camera calibration and distortion coefficients using the cv2.calibrateCamera() function. I applied this distortion correction to the test image using the cv2.undistort() function and obtained this result:
In [4]:
# performs the camera calibration, image distortion correction and
# returns the undistorted image
def cal_undistort(img, objpoints, imgpoints):
# Use cv2.calibrateCamera() and cv2.undistort()
gray = cv2.cvtColor(img,cv2.COLOR_BGR2GRAY)
ret, corners = cv2.findChessboardCorners(gray, (8,6), None)
img = cv2.drawChessboardCorners(img, (8,6), corners, ret)
ret, mtx, dist, rvecs, tvecs = cv2.calibrateCamera(objpoints, imgpoints, gray.shape[::-1], None, None)
undist = cv2.undistort(img, mtx, dist, None, mtx)
return undist, mtx, dist
# use first image as an example
img = cv2.imread(images[0])
undistorted, mtx, dist = cal_undistort(img, objpoints, imgpoints)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(undistorted)
ax2.set_title('Undistorted Image', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [5]:
def corners_unwarp(img, nx, ny, mtx, dist):
# Use the OpenCV undistort() function to remove distortion
undist = cv2.undistort(img, mtx, dist, None, mtx)
# Convert undistorted image to grayscale
gray = cv2.cvtColor(undist, cv2.COLOR_BGR2GRAY)
# Search for corners in the grayscaled image
ret, corners = cv2.findChessboardCorners(gray, (nx, ny), None)
if ret == True:
# If we found corners, draw them! (just for fun)
cv2.drawChessboardCorners(undist, (nx, ny), corners, ret)
# Choose offset from image corners to plot detected corners
# This should be chosen to present the result at the proper aspect ratio
# My choice of 100 pixels is not exact, but close enough for our purpose here
offset = 100 # offset for dst points
# Grab the image shape
img_size = (gray.shape[1], gray.shape[0])
# For source points I'm grabbing the outer four detected corners
src = np.float32([corners[0], corners[nx-1], corners[-1], corners[-nx]])
# For destination points, I'm arbitrarily choosing some points to be
# a nice fit for displaying our warped result
# again, not exact, but close enough for our purposes
dst = np.float32([[offset, offset], [img_size[0]-offset, offset],
[img_size[0]-offset, img_size[1]-offset],
[offset, img_size[1]-offset]])
# Given src and dst points, calculate the perspective transform matrix
M = cv2.getPerspectiveTransform(src, dst)
# Warp the image using OpenCV warpPerspective()
warped = cv2.warpPerspective(undist, M, img_size)
# Return the resulting image and matrix
return warped, M
nx = 9
ny = 5
w, m = corners_unwarp(img, nx, ny, mtx, dist)
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(w)
ax2.set_title('Undistorted and Warped Image', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
Let's apply the distortion correction to one of the test images. It is clear the shape of the car hood has changed after undistortion.
| Sample Image | Undistorted Image |
|---|---|
 |
 |
Thresholding¶
In this section, we'll describe how we used color transforms, gradients or other methods to create a thresholded binary image. We used the most challengling image (with shadows) to create the pipeline.
In [6]:
sample_img = mpimg.imread('test_images/test5.jpg')
plt.imshow(sample_img)
Out[6]:
Color Space Channel¶
Let's visualize all possible color space channels for this image.
In [7]:
fig, axs = plt.subplots(2,3, figsize=(14, 8))
fig.subplots_adjust(hspace = .2, wspace=.001)
axs = axs.ravel()
sample_R = sample_img[:,:,0]
sample_G = sample_img[:,:,1]
sample_B = sample_img[:,:,2]
sample_H = cv2.cvtColor(sample_img, cv2.COLOR_RGB2HSV)[:,:,0]
sample_S = cv2.cvtColor(sample_img, cv2.COLOR_RGB2HSV)[:,:,1]
sample_V = cv2.cvtColor(sample_img, cv2.COLOR_RGB2HSV)[:,:,2]
axs[0].imshow(sample_R, cmap='gray')
axs[0].set_title('RGB R-channel', fontsize=20)
axs[1].imshow(sample_G, cmap='gray')
axs[1].set_title('RGB G-Channel', fontsize=20)
axs[2].imshow(sample_B, cmap='gray')
axs[2].set_title('RGB B-channel', fontsize=20)
axs[3].imshow(sample_H, cmap='gray')
axs[3].set_title('HSV H-Channel', fontsize=20)
axs[4].imshow(sample_S, cmap='gray')
axs[4].set_title('HSV S-channel', fontsize=20)
axs[5].imshow(sample_V, cmap='gray')
axs[5].set_title('HSV V-Channel', fontsize=20)
Out[7]:
I used a combination of color and gradient thresholds to generate a binary image. Here's an example of applying thresholding on some color spaces to produce thresholded binary images.
In [8]:
def get_binary(img, conv_type="gray", thresh = (180, 255)):
if conv_type == "gray":
img = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
if conv_type == "R":
img = img[:,:,0]
if conv_type == "G":
img = img[:,:,1]
if conv_type == "B":
img = img[:,:,2]
if conv_type == "H":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HSV)
img = img[:,:,0]
if conv_type == "S":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HSV)
img = img[:,:,1]
if conv_type == "V":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HSV)
img = img[:,:,2]
if conv_type == "HLS_H":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,0]
if conv_type == "HLS_L":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,1]
if conv_type == "HLS_S":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,2]
if conv_type == "LAB_L":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,0]
if conv_type == "LAB_A":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,1]
if conv_type == "LAB_B":
img = cv2.cvtColor(img, cv2.COLOR_RGB2HLS)
img = img[:,:,2]
if conv_type == "LUV_L":
img = cv2.cvtColor(img, cv2.COLOR_RGB2Luv)
img = img[:,:,0]
if conv_type == "LUV_U":
img = cv2.cvtColor(img, cv2.COLOR_RGB2Luv)
img = img[:,:,1]
if conv_type == "LUV_V":
img = cv2.cvtColor(img, cv2.COLOR_RGB2Luv)
img = img[:,:,2]
binary = np.zeros_like(img)
binary[(img > thresh[0]) & (img <= thresh[1])] = 1
return binary
In [9]:
plt.imshow(get_binary(sample_img, conv_type="gray", thresh = (200, 255)), cmap="gray")
plt.title("Gray-channel", fontsize=20)
Out[9]:
In [10]:
fig, axs = plt.subplots(5,3, figsize=(12, 15))
fig.subplots_adjust(hspace = .2, wspace=.001)
axs = axs.ravel()
sample_R = get_binary(sample_img, conv_type="R", thresh = (220, 255))
sample_G = get_binary(sample_img, conv_type="G", thresh = (200, 255))
sample_B = get_binary(sample_img, conv_type="B", thresh = (200, 255))
sample_H = get_binary(sample_img, conv_type="H", thresh = (90, 255))
sample_S = get_binary(sample_img, conv_type="S", thresh = (90, 255))
sample_V = get_binary(sample_img, conv_type="V", thresh = (90, 255))
sample_HH = get_binary(sample_img, conv_type="HLS_H", thresh = (90, 255))
sample_LL = get_binary(sample_img, conv_type="HLS_L", thresh = (90, 255))
sample_SS = get_binary(sample_img, conv_type="HLS_S", thresh = (90, 255))
sample_LAB_L = get_binary(sample_img, conv_type="LAB_L", thresh = (155, 220))
sample_A = get_binary(sample_img, conv_type="LAB_A", thresh = (155, 220))
sample_LAB_B = get_binary(sample_img, conv_type="LAB_B", thresh = (155, 220))
sample_LUV_L = get_binary(sample_img, conv_type="LUV_L", thresh = (225, 255))
sample_LUV_U = get_binary(sample_img, conv_type="LUV_U", thresh = (225, 255))
sample_LUV_V = get_binary(sample_img, conv_type="LUV_V", thresh = (225, 255))
plot_imgs = [sample_R, sample_G, sample_B, sample_H, sample_S, sample_V, sample_HH, sample_LL, sample_SS,
sample_LAB_L, sample_A, sample_LAB_B, sample_LUV_L, sample_LUV_U, sample_LUV_V]
titles = ['RGB R-channel', 'RGB G-Channel', 'RGB B-channel', 'HSV H-Channel', 'HSV S-channel', 'HSV V-Channel',
'HLS H-Channel', 'HLS L-Channel', 'HLS S-Channel', 'LAB L-Channel', 'LAB A-Channel', 'LAB B-Channel',
'LUV L--Channel', 'LUV U--Channel', 'LUV V--Channel']
for idx, plot_img in zip(range(15),plot_imgs):
axs[idx].imshow(plot_img, cmap='gray')
axs[idx].set_title(titles[idx], fontsize=20)
It turned out that R-channel in RGB color space and S-channel in HLS color space have the best performances. However, when I used each one of them as thresholds, the thresholded image always picked up some extra noise caused by the shadows on the road. So I decided to seperate white and yellow lines. More specifically, I used B channel from Lab with thresholds between 155 and 200 for yellow lines and L channel from LUV with thresholds between 225 and 255 for white lines. See an example below for an image and the output image with Sobel Operator.
In [11]:
# Sobel Operator
def abs_sobel_thresh(img, orient='x', sobel_kernel=3, thresh=(0,255)):
# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
# Apply x or y gradient with the OpenCV Sobel() function
# and take the absolute value
if orient == 'x':
abs_sobel = np.absolute(cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel))
if orient == 'y':
abs_sobel = np.absolute(cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel))
# Rescale back to 8 bit integer
scaled_sobel = np.uint8(255*abs_sobel/np.max(abs_sobel))
# Create a copy and apply the threshold
binary_output = np.zeros_like(scaled_sobel)
# Here I'm using inclusive (>=, <=) thresholds, but exclusive is ok too
binary_output[(scaled_sobel >= thresh[0]) & (scaled_sobel <= thresh[1])] = 1
# Return the result
return binary_output
In [12]:
grad_binary = abs_sobel_thresh(sample_img, orient='x', thresh=(10,100))
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(sample_img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(grad_binary, cmap='gray')
ax2.set_title('Thresholded Gradient', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [13]:
# magnitude of gradient
def mag_thresh(img, sobel_kernel=3, thresh=(0, 255)):
# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
# Take both Sobel x and y gradients
sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
# Calculate the gradient magnitude
gradmag = np.sqrt(sobelx**2 + sobely**2)
# Rescale to 8 bit
scale_factor = np.max(gradmag)/255
gradmag = (gradmag/scale_factor).astype(np.uint8)
# Create a binary image of ones where threshold is met, zeros otherwise
binary_output = np.zeros_like(gradmag)
binary_output[(gradmag >= thresh[0]) & (gradmag <= thresh[1])] = 1
# Return the binary image
return binary_output
This example below shows an image and the output image after applying thresholding of magnitude of gradient.
In [14]:
mag_binary = mag_thresh(sample_img, sobel_kernel=3, thresh=(30, 100))
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(sample_img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(mag_binary, cmap='gray')
ax2.set_title('Thresholded Magnitude', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [15]:
# direction of the gradient
def dir_threshold(img, sobel_kernel=3, thresh=(0, np.pi/2)):
# Grayscale
gray = cv2.cvtColor(img, cv2.COLOR_RGB2GRAY)
# Calculate the x and y gradients
sobelx = cv2.Sobel(gray, cv2.CV_64F, 1, 0, ksize=sobel_kernel)
sobely = cv2.Sobel(gray, cv2.CV_64F, 0, 1, ksize=sobel_kernel)
# Take the absolute value of the gradient direction,
# apply a threshold, and create a binary image result
absgraddir = np.arctan2(np.absolute(sobely), np.absolute(sobelx))
binary_output = np.zeros_like(absgraddir)
binary_output[(absgraddir >= thresh[0]) & (absgraddir <= thresh[1])] = 1
# Return the binary image
return binary_output
This example below shows an image and the output image after applying thresholding of direction of gradient.
In [16]:
dir_binary = dir_threshold(sample_img, sobel_kernel=15, thresh=(0.7, 1.3))
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(sample_img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(dir_binary, cmap='gray')
ax2.set_title('Thresholded Grad. Dir.', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
If we combine all above steps as a single pipeline, the output image looks like the one below.
In [17]:
ksize = 3 # Choose a larger odd number to smooth gradient measurements
# Apply each of the thresholding functions
gradx = abs_sobel_thresh(sample_img, orient='x', sobel_kernel=ksize, thresh=(0, 255))
grady = abs_sobel_thresh(sample_img, orient='y', sobel_kernel=ksize, thresh=(0, 255))
mag_binary = mag_thresh(sample_img, sobel_kernel=ksize, thresh=(30, 100))
dir_binary = dir_threshold(sample_img, sobel_kernel=ksize, thresh=(0.7, 1.3))
combined = np.zeros_like(dir_binary)
# both the x and y gradients meet the threshold criteria, or the gradient magnitude
# and direction are both within their threshold values.
# combined[((gradx == 1) & (grady == 1)) | ((mag_binary == 1) & (dir_binary == 1))] = 1
combined[ ((mag_binary == 1) & (dir_binary == 1))] = 1
plt.imshow(combined, cmap='gray')
# plt.imshow(dir_binary, cmap='gray')
Out[17]:
In [157]:
def thresholding_pipeline(img, b_thresh=(155, 200), l_thresh=(225, 255), sx_thresh=(20, 100)):
b_binary = get_binary(img, conv_type="LAB_B", thresh = b_thresh)
l_binary = get_binary(img, conv_type="LUV_L", thresh = l_thresh)
# Sobel x
hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS).astype(np.float)
l_channel = hls[:,:,1]
sobelx = cv2.Sobel(l_channel, cv2.CV_64F, 1, 0) # Take the derivative in x
abs_sobelx = np.absolute(sobelx) # Absolute x derivative to accentuate lines away from horizontal
scaled_sobel = np.uint8(255*abs_sobelx/np.max(abs_sobelx))
# Threshold x gradient
sxbinary = np.zeros_like(scaled_sobel)
sxbinary[(scaled_sobel >= sx_thresh[0]) & (scaled_sobel <= sx_thresh[1])] = 1
# Stack each channel
combined_binary = np.zeros_like(sxbinary)
combined_binary[ (b_binary == 1) | (l_binary == 1) | (sxbinary == 1)] = 1
return combined_binary
Let's examine the original image together with the output image with our pipeline. It is clear that we are able to distinguish lane lines from the its surroundings.
In [158]:
result = thresholding_pipeline(sample_img)
# Plot the result
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(sample_img)
ax1.set_title('Original Image', fontsize=20)
ax2.imshow(result, cmap='gray')
ax2.set_title('Pipeline Result', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
In [164]:
def thresholding_pipeline(img, s_thresh=(90, 255), sx_thresh=(20, 100)):
s_binary = get_binary(img, conv_type="HLS_S", thresh = s_thresh)
# Sobel x
hls = cv2.cvtColor(img, cv2.COLOR_RGB2HLS).astype(np.float)
l_channel = hls[:,:,1]
sobelx = cv2.Sobel(l_channel, cv2.CV_64F, 1, 0) # Take the derivative in x
abs_sobelx = np.absolute(sobelx) # Absolute x derivative to accentuate lines away from horizontal
scaled_sobel = np.uint8(255*abs_sobelx/np.max(abs_sobelx))
# Threshold x gradient
sxbinary = np.zeros_like(scaled_sobel)
sxbinary[(scaled_sobel >= sx_thresh[0]) & (scaled_sobel <= sx_thresh[1])] = 1
# Stack each channel
combined_binary = np.zeros_like(sxbinary)
combined_binary[(s_binary == 1) | (sxbinary == 1)] = 1
return combined_binary
Perspective Transform¶
Next, we'll demonstrate how we performed a perspective transform on an image.
In [165]:
undist_sample = cv2.undistort(sample_img, mtx, dist, None, mtx)
In [166]:
plt.imshow(undist_sample)
Out[166]:
I created a lane_unwarp() function takes as inputs an image (img), as well as source (src) and destination (dst) points. I chose to hardcode the source and destination points.
In [167]:
def lane_unwarp(img, src, dst):
undist = cv2.undistort(img, mtx, dist, None, mtx)
img_size = (undist.shape[1], undist.shape[0])
# use cv2.getPerspectiveTransform() to get M, the transform matrix, and Minv, the inverse
M = cv2.getPerspectiveTransform(src, dst)
Minv = cv2.getPerspectiveTransform(dst, src)
# use cv2.warpPerspective() to warp your image to a top-down view
warped = cv2.warpPerspective(undist, M, img_size, flags=cv2.INTER_LINEAR)
return undist, warped, M, Minv
In [168]:
h,w = undist_sample.shape[:2]
# define source and destination points for transform
src = np.float32([(610,450),
(710,450),
(200,700),
(1100,700)])
dst = np.float32([(450,0),
(w-450,0),
(450,h),
(w-450,h)])
undist, warped, M, Minv = lane_unwarp(sample_img, src, dst)
The images below are to verify that my perspective transform was working as expected by drawing the src and dst points onto a test image and its warped counterpart. Clearly, the lines appear parallel in the warped image.
In [169]:
f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
f.tight_layout()
ax1.imshow(sample_img)
ax1.set_title('Original Image', fontsize=20)
x = [src[0][0],src[2][0],src[3][0],src[1][0],src[0][0]]
y = [src[0][1],src[2][1],src[3][1],src[1][1],src[0][1]]
ax1.plot(x, y, color='green', alpha=0.5, linewidth=3, solid_capstyle='round', zorder=2)
ax1.set_ylim([h,0])
ax1.set_xlim([0,w])
ax2.imshow(warped)
ax2.set_title('Undistorted and Warped Image', fontsize=20)
plt.subplots_adjust(left=0., right=1, top=0.9, bottom=0.)
Color Thresholding & Perspective Transforming¶
We're gonna combine our previous steps - Color Thresholding and Perspective Transforming - to process all the test images.
In [170]:
def pipeline(img):
undist, warped, M, Minv = lane_unwarp(img, src, dst)
combined_binary = thresholding_pipeline(warped)
return undist, combined_binary, Minv
In [7]:
images = glob.glob('./test_images/*.jpg')
print("Number of test images: ", len(images))
The following images demonstarte all the test images after applying color thresholding and perspective transform.
In [171]:
fig, axs = plt.subplots(len(images),2, figsize=(8, 15))
fig.subplots_adjust(hspace = .2, wspace=.001)
axs = axs.ravel()
i = 0
for image in images:
img = cv2.imread(image)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
undist, combined_binary, Minv = pipeline(img)
axs[i].imshow(img)
axs[i].axis('off')
i += 1
axs[i].imshow(combined_binary, cmap='gray')
axs[i].axis('off')
i += 1
Fitting a Polynomial¶
By looking at the histogram of the sample image, I used sliding window technique and implemented both sliding_window_polyfit and polyfit_using_prev_fit to fit my lane lines with a 2nd order polynomial.
In [28]:
def sliding_window_polyfit(img):
# Take a histogram of the bottom half of the image
histogram = np.sum(img[img.shape[0]//2:,:], axis=0)
# Find the peak of the left and right halves of the histogram
# These will be the starting point for the left and right lines
midpoint = np.int(histogram.shape[0]//2)
quarter_point = np.int(midpoint//2)
# Previously the left/right base was the max of the left/right half of the histogram
# this changes it so that only a quarter of the histogram (directly to the left/right) is considered
leftx_base = np.argmax(histogram[quarter_point:midpoint]) + quarter_point
rightx_base = np.argmax(histogram[midpoint:(midpoint+quarter_point)]) + midpoint
# print('base pts:', leftx_base, rightx_base)
# Choose the number of sliding windows
nwindows = 10
# Set height of windows
window_height = np.int(img.shape[0]/nwindows)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = img.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Current positions to be updated for each window
leftx_current = leftx_base
rightx_current = rightx_base
# Set the width of the windows +/- margin
margin = 80
# Set minimum number of pixels found to recenter window
minpix = 40
# Create empty lists to receive left and right lane pixel indices
left_lane_inds = []
right_lane_inds = []
# Rectangle data for visualization
rectangle_data = []
# Step through the windows one by one
for window in range(nwindows):
# Identify window boundaries in x and y (and right and left)
win_y_low = img.shape[0] - (window+1)*window_height
win_y_high = img.shape[0] - window*window_height
win_xleft_low = leftx_current - margin
win_xleft_high = leftx_current + margin
win_xright_low = rightx_current - margin
win_xright_high = rightx_current + margin
rectangle_data.append((win_y_low, win_y_high, win_xleft_low, win_xleft_high, win_xright_low, win_xright_high))
# Identify the nonzero pixels in x and y within the window
good_left_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xleft_low) & (nonzerox < win_xleft_high)).nonzero()[0]
good_right_inds = ((nonzeroy >= win_y_low) & (nonzeroy < win_y_high) & (nonzerox >= win_xright_low) & (nonzerox < win_xright_high)).nonzero()[0]
# Append these indices to the lists
left_lane_inds.append(good_left_inds)
right_lane_inds.append(good_right_inds)
# If you found > minpix pixels, recenter next window on their mean position
if len(good_left_inds) > minpix:
leftx_current = np.int(np.mean(nonzerox[good_left_inds]))
if len(good_right_inds) > minpix:
rightx_current = np.int(np.mean(nonzerox[good_right_inds]))
# Concatenate the arrays of indices
left_lane_inds = np.concatenate(left_lane_inds)
right_lane_inds = np.concatenate(right_lane_inds)
# Extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
left_fit, right_fit = (None, None)
# Fit a second order polynomial to each
if len(leftx) != 0:
left_fit = np.polyfit(lefty, leftx, 2)
if len(rightx) != 0:
right_fit = np.polyfit(righty, rightx, 2)
return left_fit, right_fit, left_lane_inds, right_lane_inds, rectangle_data, histogram
In [172]:
undist, sample_binary, Minv = pipeline(sample_img)
left_fit, right_fit, left_lane_inds, right_lane_inds, rectangle_data, histogram = sliding_window_polyfit(sample_binary)
In [173]:
plt.plot(histogram)
Out[173]:
The following images show the result from sliding_window_polyfit and polyfit_using_prev_fit respectively.
In [174]:
h = sample_img.shape[0]
left_fit_x_int = left_fit[0]*h**2 + left_fit[1]*h + left_fit[2]
right_fit_x_int = right_fit[0]*h**2 + right_fit[1]*h + right_fit[2]
# Create an output image to draw on and visualize the result
out_img = np.uint8(np.dstack((sample_binary, sample_binary, sample_binary))*255)
# Generate x and y values for plotting
ploty = np.linspace(0, sample_binary.shape[0]-1, sample_binary.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
for rect in rectangle_data:
# Draw the windows on the visualization image
cv2.rectangle(out_img,(rect[2],rect[0]),(rect[3],rect[1]),(0,255,0), 2)
cv2.rectangle(out_img,(rect[4],rect[0]),(rect[5],rect[1]),(0,255,0), 2)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = sample_binary.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
out_img[nonzeroy[left_lane_inds], nonzerox[left_lane_inds]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds], nonzerox[right_lane_inds]] = [100, 200, 255]
plt.imshow(out_img)
plt.plot(left_fitx, ploty, color='yellow')
plt.plot(right_fitx, ploty, color='yellow')
Out[174]:
In [116]:
def polyfit_using_prev_fit(binary_warped, left_fit_prev, right_fit_prev):
nonzero = binary_warped.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
margin = 80
left_lane_inds = ((nonzerox > (left_fit_prev[0]*(nonzeroy**2) + left_fit_prev[1]*nonzeroy + left_fit_prev[2] - margin)) &
(nonzerox < (left_fit_prev[0]*(nonzeroy**2) + left_fit_prev[1]*nonzeroy + left_fit_prev[2] + margin)))
right_lane_inds = ((nonzerox > (right_fit_prev[0]*(nonzeroy**2) + right_fit_prev[1]*nonzeroy + right_fit_prev[2] - margin)) &
(nonzerox < (right_fit_prev[0]*(nonzeroy**2) + right_fit_prev[1]*nonzeroy + right_fit_prev[2] + margin)))
# Again, extract left and right line pixel positions
leftx = nonzerox[left_lane_inds]
lefty = nonzeroy[left_lane_inds]
rightx = nonzerox[right_lane_inds]
righty = nonzeroy[right_lane_inds]
left_fit_new, right_fit_new = (None, None)
if len(leftx) != 0:
# Fit a second order polynomial to each
left_fit_new = np.polyfit(lefty, leftx, 2)
if len(rightx) != 0:
right_fit_new = np.polyfit(righty, rightx, 2)
return left_fit_new, right_fit_new, left_lane_inds, right_lane_inds
In [175]:
left_fit2, right_fit2, left_lane_inds2, right_lane_inds2 = polyfit_using_prev_fit(sample_binary, left_fit, right_fit)
In [176]:
margin = 80
# Generate x and y values for plotting
ploty = np.linspace(0, sample_binary.shape[0]-1, sample_binary.shape[0] )
left_fitx = left_fit[0]*ploty**2 + left_fit[1]*ploty + left_fit[2]
right_fitx = right_fit[0]*ploty**2 + right_fit[1]*ploty + right_fit[2]
left_fitx2 = left_fit2[0]*ploty**2 + left_fit2[1]*ploty + left_fit2[2]
right_fitx2 = right_fit2[0]*ploty**2 + right_fit2[1]*ploty + right_fit2[2]
# Create an image to draw on and an image to show the selection window
out_img = np.uint8(np.dstack((sample_binary, sample_binary, sample_binary))*255)
window_img = np.zeros_like(out_img)
# Color in left and right line pixels
nonzero = sample_binary.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
out_img[nonzeroy[left_lane_inds2], nonzerox[left_lane_inds2]] = [255, 0, 0]
out_img[nonzeroy[right_lane_inds2], nonzerox[right_lane_inds2]] = [0, 0, 255]
# Generate a polygon to illustrate the search window area (OLD FIT)
# And recast the x and y points into usable format for cv2.fillPoly()
left_line_window1 = np.array([np.transpose(np.vstack([left_fitx-margin, ploty]))])
left_line_window2 = np.array([np.flipud(np.transpose(np.vstack([left_fitx+margin, ploty])))])
left_line_pts = np.hstack((left_line_window1, left_line_window2))
right_line_window1 = np.array([np.transpose(np.vstack([right_fitx-margin, ploty]))])
right_line_window2 = np.array([np.flipud(np.transpose(np.vstack([right_fitx+margin, ploty])))])
right_line_pts = np.hstack((right_line_window1, right_line_window2))
# Draw the lane onto the warped blank image
cv2.fillPoly(window_img, np.int_([left_line_pts]), (0,255, 0))
cv2.fillPoly(window_img, np.int_([right_line_pts]), (0,255, 0))
result = cv2.addWeighted(out_img, 1, window_img, 0.3, 0)
plt.imshow(result)
plt.plot(left_fitx2, ploty, color='yellow')
plt.plot(right_fitx2, ploty, color='yellow')
Out[176]:
Calculating the radius of curvature¶
Next, we convert x and y from pixels space to meters and calcuate the radius of curvature of the lane and the position of the vehicle with respect to center.
In [177]:
def calc_curv_rad_and_center_dist(bin_img, l_fit, r_fit, l_lane_inds, r_lane_inds):
# Define conversions in x and y from pixels space to meters
ym_per_pix = 3.048/100 # meters per pixel in y dimension, lane line is 10 ft = 3.048 meters
xm_per_pix = 3.7/378 # meters per pixel in x dimension, lane width is 12 ft = 3.7 meters
left_curverad, right_curverad, center_dist = (0, 0, 0)
# Define y-value where we want radius of curvature
# I'll choose the maximum y-value, corresponding to the bottom of the image
h = bin_img.shape[0]
ploty = np.linspace(0, h-1, h)
y_eval = np.max(ploty)
# Identify the x and y positions of all nonzero pixels in the image
nonzero = bin_img.nonzero()
nonzeroy = np.array(nonzero[0])
nonzerox = np.array(nonzero[1])
# Again, extract left and right line pixel positions
leftx = nonzerox[l_lane_inds]
lefty = nonzeroy[l_lane_inds]
rightx = nonzerox[r_lane_inds]
righty = nonzeroy[r_lane_inds]
if len(leftx) != 0 and len(rightx) != 0:
# Fit new polynomials to x,y in world space
left_fit_cr = np.polyfit(lefty*ym_per_pix, leftx*xm_per_pix, 2)
right_fit_cr = np.polyfit(righty*ym_per_pix, rightx*xm_per_pix, 2)
# Calculate the new radii of curvature
left_curverad = ((1 + (2*left_fit_cr[0]*y_eval*ym_per_pix + left_fit_cr[1])**2)**1.5) / np.absolute(2*left_fit_cr[0])
right_curverad = ((1 + (2*right_fit_cr[0]*y_eval*ym_per_pix + right_fit_cr[1])**2)**1.5) / np.absolute(2*right_fit_cr[0])
# Now our radius of curvature is in meters
# Distance from center is image x midpoint - mean of l_fit and r_fit intercepts
if r_fit is not None and l_fit is not None:
car_position = bin_img.shape[1]/2
l_fit_x_int = l_fit[0]*h**2 + l_fit[1]*h + l_fit[2]
r_fit_x_int = r_fit[0]*h**2 + r_fit[1]*h + r_fit[2]
lane_center_position = (r_fit_x_int + l_fit_x_int) /2
center_dist = (car_position - lane_center_position) * xm_per_pix
return left_curverad, right_curverad, center_dist
In [178]:
rad_l, rad_r, d_center = calc_curv_rad_and_center_dist(sample_binary, left_fit,
right_fit, left_lane_inds, right_lane_inds)
In [179]:
print('Radius of curvature for example:', rad_l, 'm,', rad_r, 'm')
print('Distance from lane center for example:', d_center, 'm')
In [180]:
def draw_lane(original_img, binary_img, l_fit, r_fit, Minv):
new_img = np.copy(original_img)
if l_fit is None or r_fit is None:
return original_img
# Create an image to draw the lines on
warp_zero = np.zeros_like(binary_img).astype(np.uint8)
color_warp = np.dstack((warp_zero, warp_zero, warp_zero))
h,w = binary_img.shape
ploty = np.linspace(0, h-1, num=h)# to cover same y-range as image
left_fitx = l_fit[0]*ploty**2 + l_fit[1]*ploty + l_fit[2]
right_fitx = r_fit[0]*ploty**2 + r_fit[1]*ploty + r_fit[2]
# Recast the x and y points into usable format for cv2.fillPoly()
pts_left = np.array([np.transpose(np.vstack([left_fitx, ploty]))])
pts_right = np.array([np.flipud(np.transpose(np.vstack([right_fitx, ploty])))])
pts = np.hstack((pts_left, pts_right))
# Draw the lane onto the warped blank image
cv2.fillPoly(color_warp, np.int_([pts]), (0,255, 0))
cv2.polylines(color_warp, np.int32([pts_left]), isClosed=False, color=(255,0,255), thickness=15)
cv2.polylines(color_warp, np.int32([pts_right]), isClosed=False, color=(0,255,255), thickness=15)
# Warp the blank back to original image space using inverse perspective matrix (Minv)
newwarp = cv2.warpPerspective(color_warp, Minv, (w, h))
# Combine the result with the original image
result = cv2.addWeighted(new_img, 1, newwarp, 0.5, 0)
return result
In [181]:
sample_result = draw_lane(sample_img, sample_binary , left_fit, right_fit, Minv)
plt.imshow(sample_result)
Out[181]:
Add Text¶
We added the radius of curvature and the position of the vehicle on top of the image.
In [182]:
def put_text(img, rad_l, rad_r, center_dist):
new_img = np.copy(img)
h = new_img.shape[0]
# font = cv2.FONT_HERSHEY_DUPLEX
curv_rad = (rad_l + rad_r) / float(2)
text = 'Radius of Curvature = ' + '{:04.2f}'.format(curv_rad) + 'm'
cv2.putText(new_img, text, org=(210,70), fontFace=cv2.FONT_HERSHEY_SIMPLEX, fontScale=1.5,
color=(255,255,255), thickness=2, lineType = cv2.LINE_AA)
direction = ''
if center_dist > 0:
direction = 'right'
elif center_dist < 0:
direction = 'left'
abs_center_dist = abs(center_dist)
text = 'Vehicle is {:04.3f}'.format(abs_center_dist) + 'm ' + direction + ' of center'
cv2.putText(new_img, text, (210,120), cv2.FONT_HERSHEY_SIMPLEX, 1.5, (255,255,255), 2, cv2.LINE_AA)
return new_img
In [183]:
plt.imshow(put_text(sample_result, rad_l, rad_r, d_center))
Out[183]:
Complete Pipeline¶
Putting everthing together, we'll have a comple pipeline of detecting lane lines on the road.
In [184]:
# Define a class to receive the characteristics of each line detection
class Line():
def __init__(self):
# was the line detected in the last iteration?
self.detected = False
# x values of the last n fits of the line
self.recent_xfitted = []
#average x values of the fitted line over the last n iterations
self.bestx = None
#polynomial coefficients averaged over the last n iterations
self.best_fit = None
#polynomial coefficients for the most recent fit
self.current_fit = []
#radius of curvature of the line in some units
self.radius_of_curvature = None
#distance in meters of vehicle center from the line
self.line_base_pos = None
#difference in fit coefficients between last and new fits
self.diffs = np.array([0,0,0], dtype='float')
#number of detected pixels
self.px_count = None
def add_fit(self, fit, inds):
# add a found fit to the line, up to n
if fit is not None:
if self.best_fit is not None:
# if we have a best fit, see how this new fit compares
self.diffs = abs(fit-self.best_fit)
if (self.diffs[0] > 0.001 or self.diffs[1] > 1.0 or self.diffs[2] > 100.) and len(self.current_fit) > 0:
self.detected = False
else:
self.detected = True
self.px_count = np.count_nonzero(inds)
self.current_fit.append(fit)
if len(self.current_fit) > 5:
# throw out old fits, keep newest n
self.current_fit = self.current_fit[len(self.current_fit)-5:]
self.best_fit = np.average(self.current_fit, axis=0)
# or remove one from the history, if not found
else:
self.detected = False
if len(self.current_fit) > 0:
# throw out oldest fit
self.current_fit = self.current_fit[:len(self.current_fit)-1]
if len(self.current_fit) > 0:
# if there are still any fits in the queue, best_fit is their average
self.best_fit = np.average(self.current_fit, axis=0)
In [185]:
def detection_pipeline(img):
new_img = np.copy(img)
undist, img_bin, Minv = pipeline(new_img)
# if both left and right lines were detected last frame, use polyfit_using_prev_fit, otherwise use sliding window
if not l_line.detected or not r_line.detected:
l_fit, r_fit, l_lane_inds, r_lane_inds, rec_, hist_ = sliding_window_polyfit(img_bin)
else:
l_fit, r_fit, l_lane_inds, r_lane_inds = polyfit_using_prev_fit(img_bin, l_line.best_fit, r_line.best_fit)
# invalidate both fits if the difference in their x-intercepts isn't around 350 px (+/- 100 px)
if l_fit is not None and r_fit is not None:
# calculate x-intercept (bottom of image, x=image_height) for fits
h = img.shape[0]
l_fit_x_int = l_fit[0]*h**2 + l_fit[1]*h + l_fit[2]
r_fit_x_int = r_fit[0]*h**2 + r_fit[1]*h + r_fit[2]
x_int_diff = abs(r_fit_x_int-l_fit_x_int)
if abs(350 - x_int_diff) > 100:
l_fit = None
r_fit = None
l_line.add_fit(l_fit, l_lane_inds)
r_line.add_fit(r_fit, r_lane_inds)
# draw the current best fit if it exists
if l_line.best_fit is not None and r_line.best_fit is not None:
img_out = draw_lane(undist, img_bin, l_line.best_fit, r_line.best_fit, Minv)
rad_l, rad_r, d_center = calc_curv_rad_and_center_dist(img_bin, l_line.best_fit, r_line.best_fit,
l_lane_inds, r_lane_inds)
img_out = put_text(img_out, rad_l, rad_r, d_center)
else:
img_out = undist
return img_out
Our pipeline perform reasonably well on all the test images. Now we can apply it to the entire video!
In [186]:
fig, axs = plt.subplots(3,3, figsize=(14, 10))
fig.subplots_adjust(hspace = .2, wspace=.001)
axs = axs.ravel()
l_line = Line()
r_line = Line()
i = 0
for image in images:
img = cv2.imread(image)
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
result = detection_pipeline(img)
axs[i].imshow(result)
axs[i].axis('off')
i += 1
The results look good.
In [1]:
from moviepy.editor import VideoFileClip
from IPython.display import HTML
In [188]:
l_line = Line()
r_line = Line()
# video_input = VideoFileClip('project_video.mp4').subclip(30,50)
video_input = VideoFileClip('project_video.mp4')
video_output = 'project_video_output.mp4'
processed_video = video_input.fl_image(detection_pipeline)
%time processed_video.write_videofile(video_output, audio=False)
In [2]:
HTML("""
<video width="960" height="540" controls>
<source src="{0}">
</video>
""".format(
"https://github.com/wzding/Self_Driving_Car_Nanodegree/raw/master/Advanced-Lane-Lines/project_video_output.mp4"))
Out[2]:
Reflection¶
- Problems / issues I faced in the implementation of this project:
I started with some easy samples and the results of my line detection pipeline worked well untill the vehicle entered a shaded area. Then I worked with the most changllenged image - the one with most shades - in the test images to get a feel of selecting color space and tuning the parameters. I revised my pipeline based on the results of the most changllenged image and it also worked for other images. Some of the detected lane lines are wobbly but the output has an overall precise detection.
- Where will the pipeline likely fail? What could we do to make it more robust?
My pipeline is likely fail when there are white or light color cars or white signs in front of the vehicle, because then it may consider those kinds of objects as part of the lanes. To make it more robust, possible ways include selecting certain areas in the perspective transformed image to apply color thresholding rather than the whole image.